Performance of combining techniques using rotated PSK over Nakagami-m fading channels

In this article, the performance of M-ary phase shift keying (PSK) modulation schemes over mobile-to-mobile (M2M) fading channels with equal gain combining (EGC) in cooperative networks is analyzed. Narrowband M2M fading channels under line-of-sight (LOS) propagation conditions are modeled as double Rice processes. A dual-hop amplify-and-forward relay network, where LOS components can exist in the transmission links between the source mobile station and the destination mobile station via K mobile relays, is studied. Here, the average bit error probability (BEP) is utilized to evaluate the performance of Mary PSK modulation schemes. A simple analytical approximation for the average BEP of M-ary PSK modulations over relay-based M2M fading channels with EGC is derived. The accuracy of the approximation is assessed by simulations. The presented results show that in a dual-hop relay system with EGC, the presence of LOS components in the relay links improves the systems' performance. In addition, a significant enhancement in the diversity gain can be achieved as the number of diversity branches K increases.

In recent years, multiple-input-multiple-output communication has a great demand due to its flexibility and well technical implementation. Though it has been approached by many researchers, in this paper, authors taken an approach with Nakagami-m fading channel as it is a generalized fading channel for the performance of space shift keying (SSK) modulation. Simple closed form expression for the probability of bit error of SSK modulation is presented using probability density function based method for independent and identically distributed (IID) Nakagami-m fading channel. An upper bound expression for IID and correlated Nakagami-m fading channel is also presented. Obtained probability of error are in the form of Gauss hypergeometric function, confluent hypergeometric function and Gamma function which can be numerically evaluated and verified by Monte Carlo simulation.

기존의 웨이브릿 편이 변조 시스템은 스케일링 함수(scaling function)를 1로, 웨이브릿(wavelet)을 0으로 하는 1비트 변조방법이 있고, 스케일링 함수와 웨이브릿 그리고 이 두 신호를 반전시켜서 생성된 4개의 반송파를 사용하는 2비트 변조방법이 있다. 본 논문에서는 2비트 변조방법인 4-ary 스케일링 웨이브릿 편이변조(4-ary SWSK : 4-ary scaling wavelet shift keying) 시스템을 정의하고, QPSK 시스템으로부터 정의된 시스템의 비트 에러 확률과 부호 에러 확률을 유도한다. 제안한 4-ary SWSK 성능을 분석하기 위하여, 기존의 QPSK(quadrature phase shift keying), MFSK(M-ary frequency shift keying), 그리고 제안한 방법의 비트 에러 확률 및 부호 에러 확률을 구한다. 실험결과 제안한 방법의 비트 에러 확률과 부호 에러 확률이 좋은 성능을 보였다. An algorithm of the conventional wavelet shift keying is carried out that the scaling function and wavelet are encoded to 1(mark) and 0(space) for the input binary data, respectively. Two bit modulation technique which uses four carrier frequencies is existed. Four carrier frequencies are defined as scaling function, inversed scaling function, wavelet, and inversed wavelet, which are encoded to 10, 11, 00 and 01, respectively. In this paper, we defined 4-ary SWSK (4-ary scaling wavelet shift keying) which is two bit modulation, and it is derived to the probability of bit error and symbol error of the defined system from QPSK. In order to analyze to the performance of 4-ary SWSK, we are obtained in terms of the probability of bit error and symbol error for QPSK (quadrature phase shift keying), MFSK(M-ary frequency shift keying) and proposed method. As a results of simulation, we confirmed that the proposed method was superior to the performance in terms of the probability of bit error and symbol error.

In this work, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) when used along with orthogonal space-time block coding (OSTBC) over independent but not necessarily identically distributed multiple-input multiple-output (MIMO) Nakagami-m fading channels. The derived SEP expressions account for diversity branches which may exhibit identical or distinctive power levels while their associated Nakagami indexes can take arbitrary real values not less than 1/2. Our work extends previous results pertaining to the performance analysis of OSTBC using M-ary rectangular QAM over Rayleigh fading channels and M-ary square QAM over Nakagami-m fading channels. For a MIMO diversity system with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> transmit and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> receive antennas and a corresponding set of arbitrary real-valued Nakagami indexes, our rectangular QAM SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L + 1)</sup> where L = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the total number of diversity branches.

Due to the increase in massive device connectivity and increasing demands of future technologies, the Fifth-Generation (5G) networks are expected to support high spectral efficiency and low latency. In this regard, Non-Orthogonal Multiple Access (NOMA) technique has grabbed drastic attention from researchers and industry. Furthermore, to improve the performance of the NOMA system, we have incorporated the idea of cooperative communication. This paper considers a downlink NOMA system consisting of a Base Station (BS), two relays named R1 and R2, employed with Decode and Forward (DF) protocol, one far user, and one near user. In this work, an algorithm to investigate the Symbol Error Probability (SEP) performance of cooperative downlink NOMA system with Quadrature Phase Shift Keying (QPSK) modulation in the presence of the Rayleigh channel fading environment is developed. From the simulation results, it is observed that the SEP performance of the proposed NOMA system is significantly enhanced compared to that of the existing downlink NOMA system due to cooperation from the relay nodes. In addition to that, the SEP performance analysis has been made by varying the distance between the relays and BS resulting in increased SNR and reduced SEP.

The asymptotic (M to infinity ) probability of symbol error P/sub e/,/sub m/ for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E/sub b//N/sub 0/) and E/sub b/ is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E/sub b//N/sub 0/. These channels exist for all m>or=1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we examine the bit error probability (BEP) performance of binary non-coherent modulations over L-branch selective combining (SC) diversity in frequency-flat, slowly-varying double Rice fading channels. The double Rice fading channel is constructed as the product of two independent but not identically distributed Rice processes. In addition, we assume that the double Rice processes affecting the signal received over the L branches of the diversity system are independent and identically distributed. Under these assumptions, and by using the cumulative distribution function (CDF) approach, we derive an expression for the average BEP performance of binary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK) modulations. The result elaborated is generic in that it includes the propagation environments described by RayleighxRice and double Rayleigh fading models as special cases. The result is in the form of semi-infinite range integrals, that are easy to compute numerically. Additionally, for the special case of dual-branch SC diversity, i.e., L = 2, relatively simplified expressions for the BEP performance are obtained. Moreover, illustrative numerical results are presented together with corresponding simulation quantities to check the validity of the derived analytical quantities, and analyze the impact of the fading parameters on the BEP performance. The results are useful in assessing the performance of amplify-and-forward (AF) dual-hop vehicle-to-vehicle (V2V) communications with line-of-sight (LOS) paths, and where the additive noise in the relay station can be neglected.

In this paper, the performance of diversity systems operating in flat double Hoyt fading channels is studied. A novel exact expression, in the form of double finite-range integrals, is derived for the moment generating function (MGF) of the instantaneous signal-to-noise ratio (SNR). Simplified expressions are extracted for various special cases of the underlying propagation model. By using a mixture gamma (MG) distribution in the form of triple finite sums, the probability density function (PDF) of the SNR under double Hoyt fading channels is first approximated. Capitalizing on this, an approximate closed-form expression is then derived for the corresponding MGF and its most important special cases. Furthermore, building on these results, exact and approximate solutions for the ergodic capacity (EC) and symbol error probability (SEP) of M-ary phase shift keying (MPSK) modulation schemes are studied for maximum ratio combining (MRC) diversity receivers. Additionally, a new approximate closed-form expression for the corresponding asymptotic SEP at high SNR is derived. Numerical and complementary simulation results demonstrate the validity of the obtained theoretical results as well as the accuracy of the approximations. The present study is relevant to the performance evaluation of multi-antenna wireless communication systems operating under multipath fading channels that are worse than double Rayleigh fading channels.

This paper considers the channel capacity of 60GHz wireless communications systems over Rayleigh fading channels and Ricean fading channels. The SNR and therefore capacity varies according to the communication distance. The capacity is presented for line-of-sight (LOS) and non-line-of-sight (NLOS) channels given based on a 60GHz link budget model. Phase shift keying (PSK) modulation is considered under FCC power constraints for the unlicensed 59-64GHz radio spectrum. The channel capacity over Rayleigh fading channels is compared with the capacity in additive white Gaussian noise channels. The paper also investigates the channel capacity of 60GHz wireless communications systems over Ricean fading channels and gives the channel capacity compariasion with q-ary PSK modulation over Ricean fading channel, AWGN channel and Rayleigh channel when the SNR per symbol is given. The results show that a 60GHz wireless system is more suitable for short range communications less than 100 meters rather than long distances

This paper presents bit error rate (BER) analysis of wireless sensor networks (WSNs) consisting of sensor nodes based on an IEEE 802.15.4 RF transceiver. Closed-form expressions for BER are obtained for WSNs operating over AWGN, Rayleigh and Nakagami-m fading channels. For the purpose of analysis, we consider an IEEE 802.15.4 RF transceiver using direct sequence spread spectrum-offset quadrature phase shift keying (DSSS-OQPSK) modulation under 2.4 GHz frequency band in a WSN. Analytical expressions for BER are derived for a wireless link between sensor nodes that act as a transmitter unit and a base station without considering the effect of interferers in the wireless environment. Numerical results for BER are obtained by varying the IEEE 802.15.4 standard specific physical layer parameters, such as number of bits used to represent a Zigbee symbol, number of modulation levels used in an OQPSK modulator, and various values of Rayleigh and Nakagami-m fading parameters, denoted as $$\alpha $$ ? and $$m$$ m , respectively. Moreover, optimum values of physical layer parameters are identified for improved system performance. It is found that error performance analysis of WSN shows improvement when lower number of bits is used to represent a Zigbee symbol. Specifically, under a Rayleigh fading channel which reflects a real-time WSN environment, the network exhibits better performance only when it is operated at high SNR values, i.e., BER of order $$10^{-2}$$ 10 - 2 is achieved when SNR lies in the range 5---15 dB. Also, the effect of fading parameters on network performance shows that better results are obtained for higher values of $$\alpha $$ ? and $$m$$ m for Rayleigh and Nakagami-m fading channels, respectively.

To compare the transmission system suitability for power-line communications the spectral efficiency and the required transmission power are two important fundamental factors. In this paper these two factors are studied for our proposed MMFSK (M-ary multilevel FSK) system. Spectral efficiency eta of MMFSK system is a function of number of frequency levels n, number of time chips L, number of hopping patterns h. An equation connecting eta and n, L, h is derived and quantitative relationships between these parameters are studied. As a comparison spectral efficiency of existing systems such as OFDM, MFSK, multilevel FSK are also shown. Results show that compared to ordinary OFDM systems one tenth of spectral efficiency can be achieved by the proposed system which may not be attained by the other systems. The required transmission power for a fixed error rate directly relates to the radiation power. To obtain the required transmission power, relation between error rates and signal to noise ratio should be clarified. Transmission feature between the output of the transmitter and the input of the receiver for MMFSK is same as that for MFSK and the symbol error probability at the receiver input is same. Difference in bit error rate comes from difference of symbol to bit transformation process. A consideration on the relation between bit error probability and symbol error probability in MMFSK is given and a formula representing worst case probability of bit error is derived. A comparison between the worst case bit error probability and the bit error probability obtained by a simulation is shown. Using these results it is cleared that the radiation power of MMFSK is 20~50 times smaller than that of OFDM.

This paper considers the performance analysis of constructive interference (CI) precoding technique in multi-user multiple-input single-output (MU-MISO) systems with a finite constellation phase-shift keying (PSK) input alphabet. Firstly, analytical expressions for the moment generating function (MGF) and the average of the received signal-to-noise-ratio (SNR) are derived. Then, based on the derived MGF expression the average symbol error probability (SEP) for the CI precoder with PSK signaling is calculated. In this regard, new exact and very accurate asymptotic approximation for the average SEP are provided. Building on the new performance analysis, different power allocation schemes are considered to enhance the achieved SEP. In the first scheme, power allocation based on minimizing the sum symbol error probabilities (Min-Sum) is studied, while in the second scheme the power allocation based on minimizing the maximum SEP (Min-Max) is investigated. Furthermore, new analytical expressions of the throughput and power efficiency of the CI precoding in MU-MISO systems are also derived. The numerical results in this work demonstrate that, the CI precoding outperforms the conventional interference suppression precoding techniques with an up to 20 dB gain in the transmit SNR in terms of SEP, and up to 15 dB gain in the transmit SNR in terms of the throughput. In addition, the SEP-based power allocation schemes provide additional up to 13 dB gains in the transmit SNR compared to the conventional equal power allocation scheme.

The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.

In this letter, a two-user receive diversity non-orthogonal multiple-access (NOMA) wireless communication system is considered with the transmitter utilizing a rotated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary phase-shift keying ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PSK) modulation for data modulation over correlated Rician fading channels. A maximum ratio combining scheme followed by an optimum maximum-likelihood rule is employed for received data detection at each user end. Further, a simple separation scheme is proposed to eliminate the use of successive interference cancellation at the receiver end of the NOMA system. The receiver structure is utilized to derive a closed-form expression for the symbol error probability which is minimized by obtaining the optimal rotation angle of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PSK constellation. The variations of the optimal rotation angle with system parameters are studied by numerical results which lead to novel modulation schemes for the considered system.

In this paper, the performance analysis of two different diversity models in presence of multiple interferers and co-channel interference is presented. Arbitrary number of received signals are examined and processed using these diversity techniques. The performance analysis is presented for a Partitioned Selection Diversity Combiner (PSDC) which is an Advanced Diversity Combiner (ADC) consisting of $L$ Selection Combiners (SC) followed by a Maximal Ratio Combiner (MRC). The results are also presented for another ADC consisting of a Generalized Selection Combiner (GSC) followed by an MRC. Both the models are analyzed in the presence of co-channel interference (CCI) over Nakagami-m fading channels. The signal to interference plus noise ratio (SINR) is derived. Using the obtained expressions of SINR, the Average bit error rate (ABER) expression for differential phase shift keying (DPSK) and non-coherent frequency shift keying (NCFSK) modulation techniques are derived. The ABER results are plotted and comparison is made between the two diversity models. Numerical and simulation results are done.